..  Tridiagonal(dl, d, du)

Construct a tridiagonal matrix from the lower diagonal, diagonal, and upper diagonal, respectively.  The result is of type ``Tridiagonal`` and provides efficient specialized linear solvers, but may be converted into a regular matrix with :func:`full`.


In the Julia programming language, the Tridiagonal function is used to construct a tridiagonal matrix from the lower diagonal (dl), diagonal (d), and upper diagonal (du). The resulting object is of type Tridiagonal and provides efficient specialized linear solvers. However, it can be converted into a regular matrix using the full function.

Here are some examples of using the Tridiagonal function:

  1. Create a tridiagonal matrix:

    julia> dl = [1, 2, 3, 4];
    julia> d = [5, 6, 7, 8];
    julia> du = [9, 10, 11, 12];
    julia> tridiag = Tridiagonal(dl, d, du)
    4×4 Tridiagonal{Int64,Array{Int64,1}}:
    5   9   ⋅   ⋅
    1   6  10   ⋅
    ⋅   2   7  11
    ⋅   ⋅   3   8

    This example creates a 4x4 tridiagonal matrix with the provided lower diagonal, diagonal, and upper diagonal arrays.

  2. Convert Tridiagonal to a full matrix:
    julia> full_matrix = full(tridiag)
    4×4 Array{Int64,2}:
    5  9   0   0
    1  6  10   0
    0  2   7  11
    0  0   3   8

    The full function converts the Tridiagonal object to a regular matrix.

Please note that the Tridiagonal function is commonly used in numerical algorithms involving tridiagonal matrices, such as solving systems of linear equations efficiently.

See Also

Ac_ldiv_B, Ac_ldiv_Bc, Ac_mul_B, Ac_mul_Bc, Ac_rdiv_B, Ac_rdiv_Bc, At_ldiv_B, At_ldiv_Bt, At_mul_B, At_mul_Bt, At_rdiv_B, At_rdiv_Bt, A_ldiv_Bc, A_ldiv_Bt, A_mul_B!, A_mul_Bc, A_mul_Bt, A_rdiv_Bc, A_rdiv_Bt, Bidiagonal, cond, conv2, det, diag, diagind, diagm, diff, eig, eigvals, eigvecs, expm, eye, full, inv, isdiag, ishermitian, isposdef, isposdef!, issym, istril, istriu, logabsdet, logdet, lyap, norm, qrfact, rank, repmat, rot180, rotl90, rotr90, sortrows, sqrtm, SymTridiagonal, trace, Tridiagonal, tril, tril!, triu, triu!, writedlm,

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